ranger-hooah,
If you were just recently diagnosed, and your prescription for the inhaler is recent, then it will be more difficult to get the waiver. You will be found disqualified by DoDMERB (if you haven't already), and then your file will automatically be sent to the waiver authorities. Depending on which academies you've applied for, you may need to request the waiver.
Regardless of which one it is, I would write a letter to DoDMERB explaining the circumstances behind the diagnosis, how many times you've used the inhaler and what you were doing when you needed it, and what activities you currently participate in. The wavier authorities can look at medical records all day, but the personal statement stating how you are affected can carry a lot of weight.
The wavier authorities may request some additional testing. If those tests come back positive (meaning that you do have asthma or reactive airway disease) then the chances of a waiver decrease a lot.
I don't want to sound negative, but I do want you to know what the possibilities are. If the service academy is what you want you need to stay positive and stay focused.
If you have any other questions, or this isn't clear enough, feel free to ask away!